Question

设a,b∈R,且a+b=3,那2^a+2^b+1的最小值是

Answer 1

指数是b还是b+1啊,没写清楚,现在按指数是b算吧.

a+b=3

b=3-a

2^a+2^b+1

=2^a+2^(3-a)+1

=2^a+8/2^a+1

2^a恒>0

由均值不等式,得2^a=8/2^a时,即a=3/2时,2^a+8/2^a有最小值4√2

此时2^a+2^b+1有最小值4√2+1